Simplify the following expression: $\dfrac{8r^2}{16r^3}$ You can assume $r \neq 0$.
Answer: $ \dfrac{8r^2}{16r^3} = \dfrac{8}{16} \cdot \dfrac{r^2}{r^3} $ To simplify $\frac{8}{16}$ , find the greatest common factor (GCD) of $8$ and $16$ $8 = 2 \cdot 2 \cdot 2$ $16 = 2 \cdot 2 \cdot 2 \cdot 2$ $ \mbox{GCD}(8, 16) = 2 \cdot 2 \cdot 2 = 8 $ $ \dfrac{8}{16} \cdot \dfrac{r^2}{r^3} = \dfrac{8 \cdot 1}{8 \cdot 2} \cdot \dfrac{r^2}{r^3} $ $\phantom{ \dfrac{8}{16} \cdot \dfrac{2}{3}} = \dfrac{1}{2} \cdot \dfrac{r^2}{r^3} $ $ \dfrac{r^2}{r^3} = \dfrac{r \cdot r}{r \cdot r \cdot r} = \dfrac{1}{r} $ $ \dfrac{1}{2} \cdot \dfrac{1}{r} = \dfrac{1}{2r} $